Machining Method

ABSTRACT

Using a machine tool, a workpiece is machined while periodically varying the rotational speed of a spindle thereof. Correlation data on correlation between a speed variation rate RVA of the spindle rotational speed, a speed variation period ratio RVF thereof, and vibration of a tool when machining the workpiece while periodically varying the spindle rotational speed is previously obtained. Based on the correlation data, the speed variation rate RVA and the speed variation period ratio RVF are set so that the vibration of the tool and machining accuracy are within their respective allowable ranges, and based on the set speed variation rate RVA and speed variation period ratio RVF, a variation amplitude and a variation period of the spindle rotational speed are determined. The spindle is rotated at the rotational speed varying at the determined amplitude and period with respect to a target rotational speed, thereby machining the workpiece.

BACKGROUND

1. Field of the Disclosure

The present disclosure relates to a machining method of machining aworkpiece using a machine tool, wherein the rotational speed of aspindle of the machine tool is periodically varied.

2. Background of the Disclosure

It has conventionally been well known that, when a workpiece is machinedusing a machine tool, chatter vibration deteriorates machining accuracy(in particular, surface accuracy). Such chatter vibration is roughlyclassified into forced chatter vibration and self-excited chattervibration, and it is considered that forced chatter vibration is causedby an action of an excessively large external force or bysynchronization between the frequency of an external force and theresonant frequency of a vibrating system and, on the other hand,self-excited chatter vibration is caused by continuation of cutting inwhich periodic variation in cutting resistance and periodic variation inthickness of cut enhance each other through interaction therebetween(the so-called “regeneration effect”).

Further, conventionally, as a method of suppressing self-excited chattervibration included in chatter vibration, a technique of periodicallyvarying the rotational speed of a spindle at a predetermined amplitudehas been suggested. Furthermore, a technique has been suggested in whichthe variation amplitude and the variation period of the spindlerotational speed are parameterized and the parameterized variationamplitude and variation period are changed when chatter vibrationoccurs.

Further, another technique has been suggested in which averagerotational speed candidates having the effect of suppressing chattervibration are determined in accordance with the following equation and apreset number of average rotational speed candidates closest to thecurrent rotational speed are displayed on display means so that theoperator can change the rotational speed to a desired one. Furthermore,the still another technique has been suggested in which the current setvalues are plotted on a plane whose vertical axis represents the periodand whose horizontal axis represents the average rotational speed andvalues or ranges of the period and the average rotational speed havingthe effect of suppressing chatter vibration are displayed in color onthe plane.

R=120/(m(2n−1)N),

where R is the rotational-speed variation period [s], m is the number ofcutting edges of a tool, n represents an integer, and N is the averagerotational speed of the spindle [min-1].

SUMMARY OF THE DISCLOSURE

Incidentally, in the techniques generally disclosed above, the spindlerotational speed is varied at predetermined variation amplitude andvariation period so as to break the periodicities of the variation incutting resistance and the variation in thickness of cut, and thereby,self-excited chatter vibration is suppressed. Therefore, taking intoconsideration only effective suppression of self-excited chattervibration, self-excited chatter vibration is more suppressed when thevariation amplitude of the spindle rotational speed is larger, and, tothe contrary, self-excited chatter vibration is more suppressed when thevariation period of the spindle rotational speed is shorter.

However, although increasing the variation amplitude of the spindlerotational speed provides the advantage that self-excited chattervibration can be stably suppressed, in the case of a lathe, for example,it causes a large variation in the feed amount of tool per revolution ofworkpiece, and similarly in the case of a machining center, it causes alarge variation in the feed amount per revolution of tool, and in bothcases, a problem that the surface roughness of a machined workpiecesurface is not uniform, that is, machining accuracy is deteriorated isbrought about.

The same is true for the variation period of the spindle rotationalspeed. There is the advantage that self-excited chatter vibration ismore suppressed when the variation period of the spindle rotationalspeed is shorter, whereas varying the spindle rotational speed at ashort period makes the surface roughness of a machined workpiece surfacenon-uniform, which results in deterioration of machining accuracy.Additionally, the problem of excessive energy consumption is broughtabout.

The present disclosure has been achieved in view of the above-describedcircumstances, and an object thereof is to provide a machining methodwhich enables obtaining a preferable machining accuracy whileappropriately suppressing self-excited chatter vibration.

The present disclosure relates to a machining method of, in a machinetool, machining a workpiece while periodically varying a rotationalspeed of a spindle of the machine tool, the machining method comprising:

-   -   obtaining in advance correlation data indicative of correlation        between a speed variation rate RVA of the rotational speed of        the spindle, a speed variation period ratio RVF of the        rotational speed of the spindle, and vibration occurring on a        tool during machining when the workpiece is machined while        periodically varying the rotational speed of the spindle;    -   setting values of the speed variation rate RVA and the speed        variation period ratio RVF on the basis of the obtained        correlation data so that the vibration of the tool is within an        allowable range and machining accuracy is within an allowable        range, and then determining a variation amplitude and a        variation period of the rotational speed of the spindle on the        basis of the set speed variation rate RVA and the set speed        variation period ratio RVF; and    -   rotating the spindle so that the rotational speed of the spindle        varies at the determined variation amplitude and the determined        variation period with respect to a target rotational speed,        thereby machining the workpiece,    -   wherein

RVA=N _(A) /N ₀,

and

RVF=2τ/(N ₀ ×T),

-   -   where T is the variation period [s] of the rotational speed of        the spindle, N_(A) is the variation amplitude [rad/s] of the        rotational speed of the spindle, and N₀ is the target rotational        speed, that is, an average [rad/s] of the rotational speed of        the spindle in a section T.

According to the present disclosure, first, correlation data indicativeof correlation between the speed variation rate RVA of the rotationalspeed of the spindle, the speed variation period ratio RVF of therotational speed of the spindle, and vibration occurring on a toolduring machining when a workpiece is machined while periodically varyingthe rotational speed of the spindle is obtained in advance.

This correlation data can be obtained by a machining simulation based onCAE analysis or the like using three-dimensional models of the machinetool, workpiece, and tool used for machining, or can be obtained by,during actual machining using the machine tool, the workpiece and thetool, measuring displacement (vibration) of the tool by an opticaldisplacement sensor, an accelerometer or the like.

Sequentially, the values of the speed variation rate RVA and the speedvariation period ratio RVF are set based on the obtained correlationdata so that the vibration of the tool is within an allowable range andmachining accuracy is within an allowable range, and then the vibrationamplitude and the variation period of the rotational speed of thespindle are determined based on the set speed variation rate RVA and theset speed variation period ratio RVF. Then, the spindle is rotated sothat the rotational speed thereof varies at the determined variationamplitude and the determined variation period with respect to the targetrotational speed, thereby machining the workpiece.

Thus, according to the machining method of the present disclosure, sincethe values of the speed variation rate RVA and the speed variationperiod ratio RVF are set based on the correlation data indicative of thecorrelation between the speed variation rate RVA of the rotational speedof the spindle, the speed variation period ratio RVF of the rotationalspeed of the spindle, and vibration occurring on the tool duringmachining so that the vibration of the tool is within an allowable rangeand machining accuracy is within an allowable range, a preferablemachining accuracy can be achieved while self-exited chatter vibrationis appropriately suppressed.

It is noted that, as described above, reducing the variation period ofthe rotational speed of the spindle, i.e., increasing the speedvariation period ratio RVF allows a more stable suppression ofself-exited chatter vibration, but is likely to deteriorate machiningaccuracy. On the other hand, reducing the variation amplitude of therotational speed of the spindle, i.e., reducing the speed variation rateRVA allows achievement of a more preferable machining accuracy, butleads to an incomplete suppression of self-exited chatter vibration.Therefore, taking account of these opposite actions of the variationamplitude and the variation period, when the speed variation rate RVA isset to its minimum value and the speed variation period ratio RVF is setto its maximum value within an allowable vibration range of the tool,the actions of the speed variation rate RVA and the speed variationperiod ratio RVF are balanced, which makes it possible to achieve apreferable machining accuracy while stably suppressing self-exitedchatter vibration.

On the other hand, when taking the above-described opposite actions intoconsideration, if greater importance is attached to machining accuracy,it is preferable to set both of the speed variation rate RVA and thespeed variation period ratio RVF to their respective minimum values.Thereby, a more preferable machining accuracy can be achieved whileself-exited chatter vibration is properly suppressed.

As described above, according to the machining method of the presentdisclosure, since the values of the speed variation rate RVA and thespeed variation period ratio RVF are set based on the correlation dataindicative of the correlation between the speed variation rate RVA ofthe rotational speed of the spindle, the speed variation period ratioRVF of the rotational speed of the spindle, and the vibration occurringon the tool during machining so that the vibration of the tool is withinan allowable range and machining accuracy is within an allowable range,a preferable machining accuracy is achieved while self-excited chattervibration is appropriately suppressed.

Further, when the speed variation rate RVA is set to its minimum valueand the speed variation period ratio RVF is set to its maximum valuewithin the allowable vibration range of the tool, a preferable machiningaccuracy is achieved while self-excited chatter vibration is stablysuppressed. Furthermore, when both of the speed variation rate RVA andthe speed variation period ratio RVF are set to their respective minimumvalues, a more preferable machining accuracy is achieved whileself-excited chatter vibration is properly suppressed.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawings(s) will be provided by the Office upon request andpayment of the necessary fee.

For a more complete understanding of the disclosed methods andapparatus, reference should be made to the embodiment illustrated ingreater detail on the accompanying drawings, wherein:

FIG. 1 is an explanatory diagram showing a machining model for carryingout a machining method according to one embodiment of the presentdisclosure;

FIG. 2 is an explanatory diagram for explaining a variation amplitudeand a variation period of a spindle rotational speed in the machiningmethod of the embodiment;

FIG. 3 is a state diagram showing correlation between a speed variationrate RVA, a speed variation period ratio RVF, and displacement(vibration) of a tool;

FIG. 4 is a state diagram showing the correlation between the speedvariation rate RVA, the speed variation period ratio RVF, and thedisplacement (vibration) of the tool;

FIG. 5 is an explanatory diagram showing the displacement of the toolthat results when the speed variation period ratio RVF is changed withthe speed variation rate RVA set to 0.1;

FIG. 6 is an explanatory diagram showing a state of the displacement ofthe tool that results when the speed variation rate RVA and the speedvariation period ratio RVF are set to 0.1 and 0.2, respectively;

FIG. 7 is an explanatory diagram showing a state of the displacement ofthe tool that results when the speed variation rate RVA and the speedvariation period ratio RVF are set to 0.1 and 0.4, respectively;

FIG. 8 is an explanatory diagram showing a state of the displacement ofthe tool that results when the speed variation rate RVA and the speedvariation period ratio RVF are set to 0.1 and 0.8, respectively;

FIG. 9 is an explanatory diagram showing a spindle rotational speed;

FIG. 10 is an explanatory diagram showing acceleration (vibration) ofthe tool that results when the spindle is rotated at the rotationalspeed shown in FIG. 9;

FIG. 11 is an explanatory diagram showing the frequency components ofthe acceleration (vibration) of the tool during the period variationduration shown in FIG. 9;

FIG. 12 is an explanatory diagram showing the frequency components ofthe acceleration (vibration) of the tool during the constant speedduration shown in FIG. 9;

FIG. 13 is an explanatory diagram showing a spindle rotational speed;

FIG. 14 is an explanatory diagram showing acceleration (vibration) ofthe tool that results when the spindle is rotated at the rotationalspeed shown in FIG. 13;

FIG. 15 is an explanatory diagram showing the frequency components ofthe acceleration (vibration) of the tool during the period variationduration shown in FIG. 13; and

FIG. 16 is an explanatory diagram showing the frequency components ofthe acceleration (vibration) of the tool during the constant speedduration shown in FIG. 13.

It should be understood that the drawings are not necessarily to scaleand that the disclosed embodiments are sometimes illustrateddiagrammatically and in partial views. In certain instances, detailswhich are not necessary for an understanding of the disclosed methodsand apparatus or which render other details difficult to perceive mayhave been omitted. It should be understood, of course, that thisdisclosure is not limited to the particular embodiments illustratedherein.

DETAILED DESCRIPTION

Hereinafter, a specific embodiment of the present disclosure will bedescribed with reference to the drawings.

First, a schematic model of a machine tool for carrying out a machiningmethod of this embodiment will be described. FIG. 1 is an explanatorydiagram showing the schematic model of the machine tool. As shown inFIG. 1, the machine tool 1 of this embodiment includes a base 2, a ballscrew 4 supported by the base 2 to be rotatable, a feed motor 3 whichrotates the ball screw 4 around its axis, a table 5 which is screwed tothe ball screw 4 and is moved in the axial direction of the ball screw 4(X-axis direction) by the rotation of the ball screw 4, a spindle 6disposed in an area above the table 5, a spindle motor 7 which rotatesthe spindle 6 around its axis, a controller 10 which numericallycontrols the feed motor 3 and the spindle motor 7, and a driver 11which, based on a control signal transmitted from the controller 10,supplies the motor 3 and the spindle motor 7 with power corresponding tothe control signal.

It is noted that, although, for the sake of convenience, FIG. 1 depictsonly a feed mechanism (the ball screw 4 and the feed motor 3) for movingthe table 5 in the X-axis direction, the machine tool 1 also includes afeed mechanism for moving the table 5 and the spindle 6 relative to eachother in the Y-axis and Z-axis directions shown in FIG. 1 and operationof this feed mechanism is also controlled by the controller 10 and thedriver 11.

Thus, in the machine tool 1, under the control by the controller 10, thetable 5 and the spindle 6 are moved relative to each other along thethree orthogonal axes: the X axis, the Y axis, and the Z axis by thefeed mechanisms including the feed motor 3 and the spindle motor 7.Further, a workpiece W is placed on the table 5 and a tool 8 is attachedto the spindle 6, and the table 5 and the spindle 6 are moved relativeto each other as appropriate in a state where the spindle 6 is rotatedat a predetermined rotational speed, thereby machining the workpiece W.

It is noted that, obviously, the machine tool used in the presentdisclosure is not limited to a machine tool having the above-describedconfiguration and includes, besides an NC lathe, every type of knownmachine tool that cuts and machines a workpiece through relativerotation of a tool and the workpiece.

Next, a machining method of this embodiment will be described. First ofall, the value of vibration occurring on the tool 8 when machining isperformed using the machine tool 1 while the rotational speed of thespindle 6 is varied at a predetermined variation amplitude 2×N_(A)[rad/s] and a predetermined variation period T [s] with respect to apredetermined target rotational speed (average rotational speed) N₀[rad/s] as shown in FIG. 2 is obtained in advance using the variationamplitude and the variation period as variables. Then, correlation dataindicative of correlation between a speed variation rate RVA of thespindle rotational speed, a speed variation period ratio RVF of thespindle rotational speed, and the vibration occurring on the tool 8 isobtained. It is noted that the speed variation rate RVA and the speedvariation period ratio RVF are represented by the following equations.Further, a variation waveform of the rotational speed is not limited toa triangular waveform as shown in FIG. 2, and may be a sinusoidalwaveform or a trapezoidal waveform, for example.

RVA=N _(A) /N ₀

RVF=2τ/(N ₀ ×T)

This correlation data can be obtained by a machining simulation based onCAE analysis or the like using three-dimensional models of the machinetool 1, the workpiece W, and the tool 8, or by measuring the vibrationof the tool 8 by an accelerometer, an optical displacement sensor, orthe like during actual machining using the machine tool 1, the workpieceW, and the tool 8. It is noted that cutting conditions for the machiningsimulation and the actual machining are cutting conditions which are tobe actually applied and under which self-excited chatter vibrationoccurs.

The correlation data, which is obtained by a machining simulation, isshown in FIGS. 3 and 4. FIG. 3 shows a state diagram whose horizontalaxis represents the speed variation rate RVA and whose vertical axisrepresents the speed variation period ratio RVF and which shows themagnitude (level) of displacement (vibration) of the tool 8 which iscolor-coded according to the magnitude of displacement and further isrepresented in gray scale. Further, FIG. 4 is a state diagram whosevertical axis represents the displacement of the tool 8 and whosehorizontal axes represent the speed variation rate RVA and the speedvariation period ratio RVF and which shows the magnitude of displacementof the tool 8 which is color-coded according to the magnitude ofdisplacement and represented in a three-dimensional manner and furtheris represented in gray scale. In the color coding, red becomes deeper asthe displacement becomes larger, blue becomes deeper as the displacementbecomes smaller, and the middle is yellow.

It is noted that, in the above machining simulation, the feed rate Vs ofthe tool 8 is set to 2×10⁻³ [m/s], the width of cut a to 5×10⁻³ [m], theintrinsic cutting force Kt to 300 [MPa], the dynamic mass M to 10[Ns²/m], the mechanical impedance B to 200 [Ns/m], and the dynamicrigidity K to 5×10⁵ [N/m]. In addition, as shown in FIG. 2, the averagerotational speed of the spindle 6 is set to 262 [rad/s], at whichself-excited chatter vibration occurs, and the speed variation rate RVAand the speed variation period ratio RVF are each changed in a range of0.001 or more to 1.0 or less.

The results thereof shown FIGS. 3 and 4 demonstrate that thedisplacement, i.e., vibration of the tool 8 is reduced as the speedvariation rate RVA and the speed variation period ratio RVF eachincrease. Further, the results also demonstrate that sharp suppressionof self-excited chatter vibration of the tool 8 starts near a point atwhich the speed variation rate RVA reaches 0.05 and the displacement ofthe tool 8 is well suppressed in an area in which the speed variationrate RVA is smaller than 0.05. In this connection, FIG. 5 depicts thedisplacement of the tool 8 that results when the speed variation periodratio RVF is changed with the speed variation rate RVA fixed to 0.1. Itis found that, in this case, setting the speed variation period ratioRVF to a value equal to or larger than 0.5 suppresses self-excitedchatter vibration of the tool 8.

FIG. 6 depicts a state of the displacement of the tool 8 that resultswhen the speed variation period ratio RVF is set to 0.2 with the speedvariation rate RVA set to 0.1, FIG. 7 depicts a state of thedisplacement of the tool 8 that results when the speed variation periodratio RVF is set to 0.4 with the speed variation rate RVA set to 0.1,and FIG. 8 depicts a state of the displacement of the tool 8 thatresults when the speed variation period ratio RVF is set to 0.8 with thespeed variation rate RVA set to 0.1. As seen from FIGS. 6 to 8, in thecase where the speed variation period ratio RVF is set to 0.2 or 0.4,the displacement of the tool 8 increases as time elapses, which meansthat the self-excited chatter vibration cannot be suppressed, whereas,in the case where the speed variation period ratio RVF is set to 0.8,the displacement of the tool 8 decreases as time elapses, which meansthat the self-excited chatter vibration is suppressed.

As understood from the foregoing, self-excited chatter vibration of thetool 8 can be more stably suppressed as each of the speed variation rateRVA and the speed variation period ratio RVF is increased.

Further, in this embodiment, based on the correlation data indicative ofthe correlation between the speed variation rate RVA, the speedvariation period ratio RVF, and the displacement (vibration) of the tool8, which has been obtained in the above-described manner, the speedvariation rate RVA and the speed variation period ratio RVF are set sothat the vibration of the tool 8 is within an allowable range andmachining accuracy is within an allowable range.

For example, based on the correlation data shown in FIGS. 3 and 4, sinceit is conceivable that the vibration of the tool 8 is kept within anallowable range when, as described above, the speed variation rate RVAis equal to or larger than 0.3 and the speed variation period ratio RVFis equal to or larger than 0.01, when the aspect of keeping thevibration of the tool 8 within an allowable range is taken intoconsideration, it is preferable that the speed variation rate RVA beequal to or larger than 0.3 and the speed variation period ratio RVF beequal to or larger than 0.01.

On the other hand, as understood from the above equations, increasingthe speed variation rate RVA means increasing the variation amplitude ofthe spindle rotational speed, and increasing the variation amplitude ofthe spindle rotational speed, for example, causes a great variation inthe feed amount of tool per revolution of workpiece in the case of alathe and similarly causes a great variation in the feed amount perrevolution of tool in the case of a machining center. In both cases, thesurface roughness of a machined workpiece surface tends to becomenon-uniform, that is, machining accuracy tends to be deteriorated.Therefore, when the aspect of machining accuracy is taken intoconsideration, it is preferable that the speed variation rate RVA is assmall as possible.

Further, increasing the speed variation period ratio RVF means reducingthe variation period of the spindle rotational speed, and reducing thevariation period of the spindle rotational speed, that is, varying thespindle rotational speed at a short period makes the surface roughnessof a machined workpiece surface non-uniform and, also in this case,machining accuracy tends to be deteriorated. However, the degree of theeffect on machining accuracy is smaller than that in the case ofincreasing the variation amplitude of the spindle rotational speed.

Based on the foregoing, in this embodiment, the speed variation rate RVAis set to its minimum value and the speed variation period ratio RVF isset to its maximum value within the allowable vibration range of thetool 8. For example, based on the correlation data shown in FIGS. 3 and4, the speed variation rate RVA is set to 0.3 and the speed variationperiod ratio RVF is set to 1.0.

Subsequently, based on the set speed variation rate RVA and speedvariation period ratio RVF, the variation amplitude N_(A) and thevariation period T of the spindle rotational speed are determined. Then,under control by the controller 10, the spindle 6 is rotated so that therotational speed thereof varies at the determined variation amplitudeN_(A) and variation period T with respect to the average (target)rotational speed N₀, thereby machining the workpiece W. It is noted thatthe variation amplitude N_(A) and the variation period T can becalculated using the following equations derived from the aboveequations:

N _(A) =N ₀ ×RVA,

and

T=2τ/(N ₀ ×RVF).

For example, in the above example in which N₀=262 [rad/s], RVA=0.3, andRVF=1.0, the variation amplitude N_(A) and the variation period T are asfollows:

N _(A) =N ₀ ×RVA=262×0.3=78.6 [rad/s],

and

T=2τ/(N ₀ ×RVF)=2τ/(262×1.0)=0.024 [s].

Thus, according to the machining method of this embodiment, since, basedon the correlation data indicative of the correlation between the speedvariation rate RVA of the spindle rotational speed, the speed variationperiod ratio RVF of the spindle rotational speed, and the vibrationoccurring on the tool 8 during machining, the speed variation rate RVAis set to its minimum value and the speed variation period ratio RVF isset to its maximum value within the allowable vibration range of thetool 8, a preferable machining accuracy can be achieved whileself-excited chatter vibration is stably suppressed.

It is noted that, as described above, when increasing the speedvariation period ratio RVF, that is, when varying the spindle rotationalspeed at a short period, there is the tendency that the surfaceroughness of a machined workpiece surface becomes non-uniform andmachining accuracy is deteriorated. Therefore, if greater importance isattached to the aspect of machining accuracy, both of the speedvariation rate RVA and the speed variation period ratio RVF may be setto their respective minimum values within the allowable vibration rangeof the tool 8. In this case, a more preferable machining accuracy can beachieved while self-exited chatter vibration is properly suppressed.

In this connection, FIG. 10 depicts the result of detection of thevibration of the tool 8 using an acceleration sensor when the workpieceW is machined under the above-mentioned cutting conditions whilerotating the spindle 6 at the rotational speed shown in FIG. 9. It isnoted that the rotational speed of the spindle 6 shown in FIG. 9 isperiodically varied at the speed variation rate RVA of 0.3 and the speedvariation period ratio RVF of 0.01 with the average rotational speed N₀set to 262 [rad/s] for about 6 [s] after the start of cutting and thenis fixed to a constant rotational speed. In FIG. 9, ω denotes the actualrotational speed of the spindle 6 and ω_(ref) denotes an input valueinput to the spindle motor 7.

The obtained data on the variation of the tool 8 is then subjected to aspectral analysis. FIGS. 11 and 12 depict the result of the spectralanalysis. FIG. 11 depicts the frequency components of the acceleration(vibration) of the tool 8 during the period in which the rotationalspeed is periodically varied, and FIG. 12 depicts the frequencycomponents of the acceleration (vibration) of the tool 8 during theperiod in which the rotational speed is fixed to the constant speed. Asseen from FIGS. 11 and 12, self-excited chatter vibration of the tool 8can be suppressed by periodically varying the rotational speed of thespindle 6 so that the speed variation rate RVA is 0.3 and the speedvariation period ratio RVF is 0.01.

Further, FIG. 14 depicts the result of detection of the vibration of thetool 8 using an acceleration sensor when the workpiece W is machinedunder the above-mentioned cutting conditions while rotating the spindle6 at the rotational speed shown in FIG. 13. It is noted that therotational speed of the spindle 6 shown in FIG. 13 is periodicallyvaried at the speed variation rate RVA of 0.4 and the speed variationperiod ratio RVF of 0.02 with the average rotational speed N₀ set to 262[rad/s] for about 5 [s] after the start of cutting, and then is fixed toa constant rotational speed. In FIG. 13, ω denotes the actual rotationalspeed of the spindle 6 and ω_(ref) denotes an input value input to thespindle motor 7.

The obtained data on the variation of the tool 8 is then subjected to aspectral analysis. FIGS. 15 and 16 depict the result of the spectralanalysis. FIG. 15 depicts the frequency components of the acceleration(vibration) of the tool 8 during the period in which the rotationalspeed is periodically varied, and FIG. 16 depicts the frequencycomponents of the acceleration (vibration) of the tool 8 during theperiod in which the rotational speed is fixed to the constant speed. Asseen from FIGS. 15 and 16, self-excited chatter vibration of the tool 8can be suppressed by periodically varying the rotational speed of thespindle 6 so that the speed variation rate RVA is 0.4 and the speedvariation period ratio RVF is 0.02.

As described in detail above, according to the machining method of thisembodiment, since, based on the correlation data indicative of thecorrelation between the speed variation rate RVA of the spindlerotational speed, the speed variation period ratio RVF of the spindlerotational speed, and the vibration occurring on the tool duringmachining, the values of the speed variation rate RVA and the speedvariation period ratio RVF are set so that the vibration of the tool iswithin an allowable range and machining accuracy is within an allowablerange, that is, within an allowable vibration range of the tool, thespeed variation rate RVA is set to its minimum value and the speedvariation period ratio RVF is set to its maximum value or both of thespeed variation rate RVA and the speed variation period ratio RVF areset to their respective minimum values, a preferable machining accuracycan be achieved while self-excited chatter vibration is appropriatelysuppressed.

Thus, although a specific embodiment of the present disclosure has beendescribed, the present disclosure is not limited to the above.

For example, although, in the above embodiment, within an allowablevibration range of the tool 8, the speed variation rate RVA is set toits minimum value and the speed variation period ratio RVF is set to itsmaximum value, or both of the speed variation rate RVA and the speedvariation period ratio RVF are set to their respective minimum values,the present disclosure is not limited thereto, and each of the speedvariation rate RVA and the speed variation period ratio RVF may take anyvalue as long as the vibration of the tool is within an allowable rangeand machining accuracy is within an allowable range.

What is claimed is:
 1. A machining method of machining a workpiece usinga machine tool while periodically varying a rotational speed of aspindle of the machine tool, the machining method comprising: obtainingin advance correlation data indicative of correlation between a speedvariation rate RVA of the rotational speed of the spindle, a speedvariation period ratio RVF of the rotational speed of the spindle, andvibration occurring on a tool during machining when the workpiece ismachined while periodically varying the rotational speed of the spindle;setting values of the speed variation rate RVA and the speed variationperiod ratio RVF on the basis of the obtained correlation data so thatthe vibration of the tool is within an allowable range and machiningaccuracy is within an allowable range, and then determining a variationamplitude and a variation period of the rotational speed of the spindleon the basis of the set speed variation rate RVA and the set speedvariation period ratio RVF; and rotating the spindle so that therotational speed of the spindle varies at the determined variationamplitude and the determined variation period with respect to a targetrotational speed, thereby machining the workpiece, whereinRVA=N _(A) /N ₀,andRVF=2τ/(N ₀ ×T), where T is the variation period [s] of the rotationalspeed of the spindle, N_(A) is the variation amplitude [rad/s] of therotational speed of the spindle, and N₀ is the target rotational speed[rad/s].
 2. The machining method of claim 1, wherein: when setting thevalue of the speed variation rate RVA and the value of the speedvariation period ratio RVF on the basis of the correlation data, thespeed variation rate RVA is set to its minimum value and the speedvariation period ratio RVF is set to its maximum value within anallowable vibration range of the tool.
 3. The machining method of claim1, wherein: when setting the value of the speed variation rate RVA andthe value of the speed variation period ratio RVF on the basis of thecorrelation data, both of the speed variation rate RVA and the speedvariation period ratio RVF are set to their respective minimum valueswithin an allowable vibration range of the tool.
 4. The machining methodof claim 1, wherein the correlation data is obtained by a machiningsimulation using a three-dimensional model of the machine tool.
 5. Themachining method of claim 2, wherein the correlation data is obtained bya machining simulation using a three-dimensional model of the machinetool.
 6. The machining method of claim 3, wherein the correlation datais obtained by a machining simulation using a three-dimensional model ofthe machine tool.
 7. The machining method of claim 1, wherein thecorrelation data is obtained by actual machining using the machine tool.8. The machining method of claim 2, wherein the correlation data isobtained by actual machining using the machine tool.
 9. The machiningmethod of claim 3, wherein the correlation data is obtained by actualmachining using the machine tool.